Nevanlinna-Pick interpolation for $C+BH^\infty$

Mrinal Raghupathi

Published 2008-03-09, updated 2008-09-21Version 3

Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain weak*-closed ideal in $H^\infty_B$ and use this to prove an analogue of the Nevanlinna-Pick interpolation theorem.